## Exact Solution and Correlations of a Quantum Dimer Model on the Checkerboard Lattice

### Abstract

We present analytic results for a special dimer model on the {\em non-bipartite} and {\em non-planar} checkerboard lattice that does not allow for parallel dimers surrounding diagonal links. We {\em exactly} calculate the number of closed packed dimer coverings on finite checkerboard lattices under periodic boundary conditions, and determine all dimer-dimer correlations. The latter are found to vanish beyond a certain distance. We find that this solvable model, despite being non-planar, is in close kinship with well-known paradigm-setting planar counterparts that allow exact mappings to $\mathbb{Z}_2$ lattice gauge theory.Comment: 9 pages, 3 figure

Topics: Condensed Matter - Strongly Correlated Electrons
Publisher: 'American Physical Society (APS)'
Year: 2020
DOI identifier: 10.1103/PhysRevB.102.020401
OAI identifier: oai:arXiv.org:2003.12084

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